An article is listed at Rs. 7,600 and the discount offered for the unit is 10%. What additional discount must be given to bring the net selling price to Rs. 5,814?
15%
Calculating Successive Discounts on Marked Price
Understanding discounts is a common topic in percentage-related problems. When multiple discounts are offered on an article, they are usually applied successively. This means the second discount is calculated on the price after the first discount has been applied, not on the original marked price.
Step-by-Step Discount Calculation
Let's break down the problem to find the additional discount needed to reach the desired net selling price. We are given the marked price of the article and the first discount percentage. We are also given the final selling price after two successive discounts. We need to find the percentage of the second discount.
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Identify the Marked Price (MP):
The initial price listed for the article is Rs. 7,600.
\(\text{MP} = \text{Rs. } 7,600\)
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Calculate the Price after the First Discount:
A discount of 10% is offered on the marked price.
\(\text{Discount Amount 1} = 10\% \text{ of MP}\)
\(\text{Discount Amount 1} = \frac{10}{100} \times 7600\)
\(\text{Discount Amount 1} = 0.10 \times 7600\)
\(\text{Discount Amount 1} = \text{Rs. } 760\)
The price after the first discount is the Marked Price minus the first discount amount.
\(\text{Price after 1st Discount} = \text{MP} - \text{Discount Amount 1}\)
\(\text{Price after 1st Discount} = 7600 - 760\)
\(\text{Price after 1st Discount} = \text{Rs. } 6,840\)
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Determine the Required Additional Discount Amount:
The net selling price (final price) is given as Rs. 5,814. The additional discount is applied to the price after the first discount (Rs. 6,840).
\(\text{Additional Discount Amount} = \text{Price after 1st Discount} - \text{Net Selling Price}\)
\(\text{Additional Discount Amount} = 6840 - 5814\)
\(\text{Additional Discount Amount} = \text{Rs. } 1,026\)
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Calculate the Additional Discount Percentage:
The additional discount percentage is calculated on the price *after* the first discount (Rs. 6,840), as this is the price before the second discount is applied.
\(\text{Additional Discount Percentage} = \frac{\text{Additional Discount Amount}}{\text{Price after 1st Discount}} \times 100\%\)
\(\text{Additional Discount Percentage} = \frac{1026}{6840} \times 100\%\)
\(\text{Additional Discount Percentage} = 0.15 \times 100\%\)
\(\text{Additional Discount Percentage} = 15\%\)
Therefore, an additional discount of 15% must be given to bring the net selling price of the article to Rs. 5,814.
Summary of Calculations
| Description | Amount (Rs.) |
|---|---|
| Marked Price (MP) | 7,600 |
| First Discount (10% of MP) | 760 |
| Price after 1st Discount | 6,840 |
| Net Selling Price (SP) | 5,814 |
| Additional Discount Amount (6840 - 5814) | 1,026 |
| Additional Discount Percentage (\(\frac{1026}{6840} \times 100\%\)) | 15% |
Revision Table: Key Terms in Discount Problems
| Term | Definition | How it's Used Here |
|---|---|---|
| Marked Price (MP) | The price listed on the article. | Starting price: Rs. 7,600. Discounts are applied to this initially. |
| Discount | A reduction in the price of an article. | Given as 10% initially, then an additional percentage. |
| Selling Price (SP) | The price at which the article is sold after discounts. | Final price is the Net Selling Price (Rs. 5,814). |
| Successive Discounts | When one discount is applied, and then another discount is applied to the reduced price. | 10% discount applied first, then an additional discount on the result. |
Additional Information on Discounts and Percentages
When dealing with percentages and discounts, it's important to remember the base on which the percentage is calculated. For the first discount, the base is the marked price. For the second (additional) discount in a successive discount scenario, the base is the price after the first discount has been subtracted.
A single equivalent discount for two successive discounts of \(d_1\%\) and \(d_2\%\) is not simply \(d_1 + d_2\). The formula for a single equivalent discount (\(D\%\)) is:
\(D = d_1 + d_2 - \frac{d_1 \times d_2}{100}\)
In this problem, we were given one discount (\(d_1 = 10\%\)) and the final selling price, and we had to find the second discount (\(d_2\)). Our approach of calculating the price after the first discount and then finding the percentage reduction to reach the final price is a direct way to solve this specific problem involving successive discounts.
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